Three-twist knot

In knot theory, the three-twist knot is the twist knot with three-half twists. ^[1]

Alexander polynomial

In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. Three-twist knot and Alexander polynomial are knot theory.

See Three-twist knot and Alexander polynomial

Chiral knot

In the mathematical field of knot theory, a chiral knot is a knot that is not equivalent to its mirror image (when identical while reversed).

See Three-twist knot and Chiral knot

In knot theory, the cinquefoil knot, also known as Solomon's seal knot or the pentafoil knot, is one of two knots with crossing number five, the other being the three-twist knot. Three-twist knot and cinquefoil knot are Alternating knots and links, knot theory, non-tricolorable knots and links, prime knots and links and Reversible knots and links.

See Three-twist knot and Cinquefoil knot

Crossing number (knot theory)

In the mathematical area of knot theory, the crossing number of a knot is the smallest number of crossings of any diagram of the knot.

See Three-twist knot and Crossing number (knot theory)

Fibered knot

In knot theory, a branch of mathematics, a knot or link K in the 3-dimensional sphere S^3 is called fibered or fibred (sometimes Neuwirth knot in older texts, after Lee Neuwirth) if there is a 1-parameter family F_t of Seifert surfaces for K, where the parameter t runs through the points of the unit circle S^1, such that if s is not equal to t then the intersection of F_s and F_t is exactly K.

See Three-twist knot and Fibered knot

Hyperbolic link

In mathematics, a hyperbolic link is a link in the 3-sphere with complement that has a complete Riemannian metric of constant negative curvature, i.e. has a hyperbolic geometry. Three-twist knot and hyperbolic link are hyperbolic knots and links and knot theory.

See Three-twist knot and Hyperbolic link

Hyperbolic volume

In the mathematical field of knot theory, the hyperbolic volume of a hyperbolic link is the volume of the link's complement with respect to its complete hyperbolic metric. Three-twist knot and hyperbolic volume are knot theory.

See Three-twist knot and Hyperbolic volume

Invertible knot

In mathematics, especially in the area of topology known as knot theory, an invertible knot is a knot that can be continuously deformed to itself, but with its orientation reversed.

See Three-twist knot and Invertible knot

Jones polynomial

In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Three-twist knot and Jones polynomial are knot theory.

See Three-twist knot and Jones polynomial

Knot theory

In topology, knot theory is the study of mathematical knots.

See Three-twist knot and Knot theory

Monic polynomial

In algebra, a monic polynomial is a non-zero univariate polynomial (that is, a polynomial in a single variable) in which the leading coefficient (the nonzero coefficient of highest degree) is equal to 1.

See Three-twist knot and Monic polynomial

Prime knot

In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable. Three-twist knot and prime knot are prime knots and links.

See Three-twist knot and Prime knot

Twist knot

In knot theory, a branch of mathematics, a twist knot is a knot obtained by repeatedly twisting a closed loop and then linking the ends together. Three-twist knot and twist knot are Double torus knots and links and twist knots.

See Three-twist knot and Twist knot

References

[1] https://en.wikipedia.org/wiki/Three-twist_knot

Also known as 5 2 knot, 5₂ knot, Three twist knot.

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Three-twist knot

Table of Contents

Alexander polynomial

Chiral knot

Cinquefoil knot

Crossing number (knot theory)

Fibered knot

Hyperbolic link

Hyperbolic volume

Invertible knot

Jones polynomial

Knot theory

Monic polynomial

Prime knot

Twist knot

See also

Alternating knots and links

Double torus knots and links

Hyperbolic knots and links

Non-tricolorable knots and links

Prime knots and links

Reversible knots and links

Twist knots

Unfibered knots and links

References